Meanings
- uncountablemathematicsThe subbranch of number theory which applies techniques from geometry to the study of algebraic numbers.
A typical approach in the geometry of numbers is to view a ring of algebraic integers as a lattice in #92;textstyle#92;mathbb#123;R#125;ⁿ; the study of these lattices provides fundamental information on algebraic numbers.
2 more examples
1969, C. G. Lekkerkerker, Geometry of Numbers, Wolters-Noordoff, North-Holland, page 1, The geometry of numbers to which this book is devoted deals with arbitrary bodies and arbitrary lattices in the n-dimensional euclidean space. Its aim is to study various quantities describing the behaviour of a body with respect to a lattice.
2006, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 181, The easy proof is obtained applying the pigeon-hole principle to α₁x_1+…+αₙx_n(mod 1)|x_i=0,…N, or by geometry of numbers by applying Minkowski's first theorem in C.2.19 to the symmetric convex body of volume 2ⁿ⁺¹ given by |X_0+α₁X_1+…αₙX_n|<N⁻ⁿ,|X_i|<N,i=1,…N.
Origin
The field was initiated by German mathematician Hermann Minkowski (1910, Geometrie der Zahlen).
Full word history & related roots →Translations
German Geometrie der Zahlen
- Geometrie der Zahlensubbranch of number theory
Italian teoria dei numeri geometrica
- teoria dei numeri geometricasubbranch of number theory
Polish geometria liczb
- geometria liczbsubbranch of number theory
Cite this entry
geometry of numbers. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/geometry%20of%20numbers
“geometry of numbers.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/geometry%20of%20numbers. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “geometry of numbers,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/geometry%20of%20numbers.
Source: geometry of numbers on Wiktionary, CC BY-SA 4.0.